Alistair sent us a very clearly-explained solution to this problem:

Fred did not cut his into four pieces, because it is the same as Charlie and David's only cut again, which means that he had eight pieces.

I have spotted that David and Charlie both cut their cubes into cuboids.

The six cubes shown were cut by: David, Belinda, Andy, Ellie, Charlie and Gill.

Thank you Alistair!

Well done too to Wafa from Jinnah Academy, Natalya from Seaton Primary, Vittal from Birchland and Samuel from Truscott Street Public School who all sent in very full solutions.